Procedural Implementation and Axiomatization of the Weighted Nonseparable Cost Value

Hui Yang,Wenna Wang,Zhengsheng Ding

doi:10.1155/2020/4674279

Abstract

The paper defines a new value called the weighted nonseparable cost value (weighted-NSC value), which divides the nonseparable cost on the ground of an exogenous attached weight and compromises egalitarianism and utilitarianism of a value flexibly. First, we construct an optimization model to minimize the deweighted variance of complaint and define its optimal solution to be the weighted-NSC value. Second, a process is set up to acquire the weighted-NSC value, which enlarges the traditional procedural values. In the process, one player’s marginal contribution is divided up by all participants rather than merely restricted within his precursors. Lastly, adopting the weight in defining a value destructs the classical symmetry. This promotes the definition of ω-symmetry for the grand-marginal normalized game to defend against the effect of weight and axiomatically sculptures the weighted-NSC value. Dual dummifying player property is also applied to characterize the new defined value.

Highlights

Consider a wireless network with n nodes. e nodes communicate with far-off destinations through the cooperation of the intermediate nodes
Sun et al [8] revealed that the ENSC value embodies utilitarianism in virtue of the player’s attitude towards the grand marginal contributions. en, we encounter the issue of equilibrate utilitarianism and egalitarianism during allocation process
Let φ: GN ⟶ Rn; we propose the corresponding axiom as follows: (i) Equal deweighted complaint property (EC): for all v ∈ GN and ω ∈ Δn, the value φ verifies that eω(i, φ) eω(j, φ), for i, j ∈ N

Summary

Introduction

Consider a wireless network with n nodes. e nodes communicate with far-off destinations through the cooperation of the intermediate nodes. Sun et al [8] revealed that the ENSC value embodies utilitarianism in virtue of the player’s attitude towards the grand marginal contributions. Yang et al [13] researched the weighted surplus division value in cooperative games. Procedural value [14] is another efficient method to compromise utilitarianism and egalitarianism on an allocation rule in the reason that one’s marginal contribution in a given permutation will be shared with his precursor. Is article designs an enlarged process to present a more detailed research of the weighted-NSC value. Is evokes us to propose ω-symmetry for the grand-marginal normalized game in order to characterize the weighted-NSC value.

Preliminaries

The Procedural Explanation

Process 1

Axiomatizations